On the equivalence of certain statements in triangles

Authors

  • Abasov Raghib Zeinal Azerbaijan State Pedagogical University

Keywords:

triangles; equivalent statements; transformations; equivalence of systems

Abstract

The equivalence of statements is one of the important concepts in mathematics. This concept plays an important role in solving some problems in both higher and school mathematics. However, sometimes these concepts are applied to problems that have different structures. In this article, general aspects are discussed to demonstrate the equivalence of some statements, as well as to solve some other problems on the topic of triangles. Furthermore, potential difficulties in this process are highlighted that still remain open problems in this field of research.

Downloads

Download data is not yet available.

References

Barra-Ferreira, E., Benevides-Soares, A., & Cabral-Lima, J. C. (2009).As Demonstrações no Ensino da Geometria: discussões sobre a formação de professores através do uso de novas tecnologias. Bolema-Mathematics Education Bulletin-Boletim De Educacao Matematica, 22(34),185–207.https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/3304.

Clark, D. M., & Pathania, S. (2023). A Full Axiomatic Development of High School Geometry (1st ed.). Springer. https://link.springer.com/book/10.1007/978-3-031-23525-2.

Chernikov, P. V. (2003). On Two Problems from International Mathematical Olympiads. Mathematics at school.

Dillon, M. I. (2018). Geometry through History. Euclidean, Hyperbolic and Projective Geometries. Springer. https://link.springer.com/book/10.1007/978-3-319-74135-2.

Heilbron, J. (2023, October 13). geometry. Encyclopedia Britannica. https://www.britannica.com/science/geometry.

Ingram, J. (2021). Thinking, Understanding, and Knowing. In Patterns in Mathematics Classroom Interaction: A Conversation Analytic Approach (pp. 77–104). Oxford University Press. https://doi.org/10.1093/oso/9780198869313.003.0005.

Lyapin, S. E., Banova, I. V., & Yuorchugova, Z. G. (1973). Collection of Problems in Elementary Algebra. Nauka.https://vk.com/wall-94378522_6265?lang=en.

Morozova, E. A., & Petrakova, I. S. (1971). International Mathematical Olympiads. Education.

Prasolov, V. V. (1986). Problems in Planimetry (Vol. 2). Nauka..

Downloads

Published

2023-12-12

How to Cite

Raghib Zeinal, A. . (2023). On the equivalence of certain statements in triangles. LUZ, 23(1), e1401. Retrieved from https://luz.uho.edu.cu/index.php/luz/article/view/1401